Hi Spencer,
the original switches are ON-OFF-ON types, for position A-0-B, or back-center-forward.
They only create an electrical connection between the center pin and one of the outer pins at a time, or no connection if at center.
When using a push button, it must be OFF-ON, means, released there is no continuity between the pins (0, center, normal flying), and pushed, it must connect. Then, it depends which two wires you connect, to the radio, if pushed means A or B. But this doesn't really matter, since you can reverse the switch (button) direction, so it either actuates something (Rescue) or not.
In other words, remove the original three position switch, see which two wires connect when actuating the momentary position, de-solder, and solder those two wire ends to the pins of the push button ... assuming it has only two pins. If it has three, it possibly connects both at the same time if pushed, or just one, another thing to check.
Kind regards
Eddi
Born to fly ...
forced to work.